State of the art and possible development of judging AIs in laws field
There has definitely been work relating to judicial sentencing:


  In a new study from the National Bureau of Economic Research, economists and computer scientists trained an algorithm to predict whether defendants were a flight risk from their rap sheet and court records using data from hundreds of thousands of cases in New York City. When tested on over a hundred thousand more cases that it hadn’t seen before, the algorithm proved better at predicting what defendants will do after release than judges.Source: M.I.T. Technology Review: How to Upgrade Judges with Machine Learning


In terms of actually trying cases to deliver a verdict of guilty or not guilty, I think that would be difficult because, although Machine Learning has been effective at outperforming humans in problems where parameters can be clearly defined, we haven't figured out how to tackle the symbol grounding problem. This means that making decisions based on language, which is less precise than mathematics, would be highly problematic. Guilty/Not Guilty is a basic True/False condition, but the rest of the language utilized in law cannot be so precisely translated.